Linear Equations and Word Problems
Word problems that lead to simple linear equations Number problems Age problems Mixture problems Miscellaneous word problems
Word problems that lead to simple linear equations
The general procedure to solve a word problem is:
1. Set the unknown.
2. Write equation from the text of the problem.
3. Solve the equation for the unknown.
Number problems
Example:  A number multiplied by 5 and divided by 4 equals twice the number decreased by 15.

Solution:   Let x denotes the number, then Example:  Split the number 61 into two parts so that quarter of the first part increased by sixth of the other
part gives 12. What are these parts?
Solution:   Let x denotes the first part of the number, then Age problems
Example:  A father is 48 years old and his son is 14.
a)  In how many years will the father be three times older then his son?
b)  How many years before was the father seven times older then his son?
Solution:   After x years     a)    48 + x = 3 · (14 + x)
48 + x = 42 + 3x
x - 3x = 42 - 48
-2x = -6 | ¸ (-2)
x = 3 years.
Before x years     b)    48 - x = 7 · (14 - x)
48 - x = 98 - 7x
7x - x = 98 - 48
6x = 50
x = 25/3 = 8 years and 4 months.
Miscellaneous word problems
Example:  If fresh grapes contain 90% water and dried 12%, how much dry grapes we get from 22 kg of fresh
grapes?
Solution:  Fresh grapes contain 90% water and 10% dry substance.
Dry grapes contain 12% water and 88% dry substance.
 22 kg of fresh grapes = x kg of dry grapes, so Example:  An amount decreased 20% and then increased 50%, what is the total increase in relation to initial
value.
 Solution:  An initial amount x decreased by 20%, The obtained amount increased by 50%, The difference in relation to the initial value x, shows increase by 20%.
Example:  From a total deducted is 5% for expenses and the remainder is equally divided to three persons.
What was the total if each person gets \$190?
 Solution:  If x denotes the total then  Example:  Into 10 liters of the liquid A poured is 4 liters of the liquid B and 6 liters of the liquid C.
From obtained mixture D poured is out 3 liters, how many liters of the liquid C remains in the mixture D?
Solution:    A + B + C = D      =>     10 l + 4 l + 6 l  = 20 l    Intermediate algebra contents 